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--- |
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library_name: transformers |
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license: other |
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license_name: lfm1.0 |
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license_link: LICENSE |
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language: |
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- en |
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pipeline_tag: text-generation |
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tags: |
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- liquid |
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- lfm2 |
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- edge |
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base_model: LiquidAI/LFM2-350M |
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--- |
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<center> |
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<div style="text-align: center;"> |
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<img |
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src="https://cdn-uploads.huggingface.co/production/uploads/61b8e2ba285851687028d395/2b08LKpev0DNEk6DlnWkY.png" |
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alt="Liquid AI" |
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style="width: 100%; max-width: 100%; height: auto; display: inline-block; margin-bottom: 0.5em; margin-top: 0.5em;" |
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/> |
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</div> |
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<div style="display: flex; justify-content: center; gap: 0.5em;"> |
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<a href="https://playground.liquid.ai/chat"> |
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<a href="https://playground.liquid.ai/"><strong>Try LFM</strong></a> • <a href="https://docs.liquid.ai/lfm"><strong>Documentation</strong></a> • <a href="https://leap.liquid.ai/"><strong>LEAP</strong></a></a> |
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</div> |
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</center> |
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# LFM2-350M-Math |
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Based on [LFM2-350M](https://huggingface.co/LiquidAI/LFM2-350M), LFM2-350M-Math is a tiny reasoning model designed for tackling tricky math problems. |
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You can find more information about other task-specific models in this [blog post](https://www.liquid.ai/blog/introducing-liquid-nanos-frontier-grade-performance-on-everyday-devices). |
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## 📄 Model details |
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**Generation parameters**: We strongly recommend using greedy decoding with a `temperature=0.6`, `top_p=0.95`, `min_p=0.1`, `repetition_penalty=1.05`. |
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**System prompt**: We recommend not using any system prompt. |
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**Supported languages**: English only. |
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**Chat template**: LFM2 uses a ChatML-like chat template as follows: |
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``` |
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<|startoftext|><|im_start|>user |
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Find the sum of all integer bases $b>9$ for which $17_{b}$ is a divisor of $97_{b}$.<|im_end|> |
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<|im_start|>assistant |
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<|cot_start|>First, we need to convert $17_{b}$ and $97_{b}$ into base 10. [...]<|im_end|> |
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``` |
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You can automatically apply it using the dedicated [`.apply_chat_template()`](https://huggingface.co/docs/transformers/en/chat_templating#applychattemplate) function from Hugging Face transformers. |
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> [!WARNING] |
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> ⚠️ The model is intended for single-turn conversations. |
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## 📈 Performance |
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Reasoning enables models to better structure their thought process, explore multiple solution strategies, and self-verify their final responses. Augmenting tiny models with extensive test-time compute in this way allows them to even solve challenging competition-level math problems. Our benchmark evaluations demonstrate that LFM2-350M-Math is highly capable for its size. |
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As we are excited about edge deployment, our goal is to limit memory consumption and latency. Our post-training recipe leverages reinforcement learning to explicitly bring down response verbosity where it is not desirable. To this end, we combine explicit reasoning budgets with difficulty-aware advantage re-weighting. Please refer to our separate [blog post](https://www.liquid.ai/research/lfm-1b-math-can-small-models-be-concise-reasoners) for a detailed post-training recipe. |
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## 🏃 How to run |
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- Hugging Face: [LFM2-350M](https://huggingface.co/LiquidAI/LFM2-350M) |
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- llama.cpp: [LFM2-350M-Math-GGUF](https://huggingface.co/LiquidAI/LFM2-350M-Math-GGUF) |
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- LEAP: [LEAP model library](https://leap.liquid.ai/models?model=lfm2-350M-math) |
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You can use the following Colab notebooks for easy inference and fine-tuning: |
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| Notebook | Description | Link | |
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|-------|------|------| |
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| Inference | Run the model with Hugging Face's transformers library. | <a href="https://colab.research.google.com/drive/1TfLUH1vpIiJE6TdZTlMxhbp95f3BNKaD?usp=sharing"><img src="https://cdn-uploads.huggingface.co/production/uploads/61b8e2ba285851687028d395/vlOyMEjwHa_b_LXysEu2E.png" width="110" alt="Colab link"></a> | |
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| SFT (TRL) | Supervised Fine-Tuning (SFT) notebook with a LoRA adapter using TRL. | <a href="https://colab.research.google.com/drive/1j5Hk_SyBb2soUsuhU0eIEA9GwLNRnElF?usp=sharing"><img src="https://cdn-uploads.huggingface.co/production/uploads/61b8e2ba285851687028d395/vlOyMEjwHa_b_LXysEu2E.png" width="110" alt="Colab link"></a> | |
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| DPO (TRL) | Preference alignment with Direct Preference Optimization (DPO) using TRL. | <a href="https://colab.research.google.com/drive/1MQdsPxFHeZweGsNx4RH7Ia8lG8PiGE1t?usp=sharing"><img src="https://cdn-uploads.huggingface.co/production/uploads/61b8e2ba285851687028d395/vlOyMEjwHa_b_LXysEu2E.png" width="110" alt="Colab link"></a> | |
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| SFT (Axolotl) | Supervised Fine-Tuning (SFT) notebook with a LoRA adapter using Axolotl. | <a href="https://colab.research.google.com/drive/155lr5-uYsOJmZfO6_QZPjbs8hA_v8S7t?usp=sharing"><img src="https://cdn-uploads.huggingface.co/production/uploads/61b8e2ba285851687028d395/vlOyMEjwHa_b_LXysEu2E.png" width="110" alt="Colab link"></a> | |
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| SFT (Unsloth) | Supervised Fine-Tuning (SFT) notebook with a LoRA adapter using Unsloth. | <a href="https://colab.research.google.com/drive/1HROdGaPFt1tATniBcos11-doVaH7kOI3?usp=sharing"><img src="https://cdn-uploads.huggingface.co/production/uploads/61b8e2ba285851687028d395/vlOyMEjwHa_b_LXysEu2E.png" width="110" alt="Colab link"></a> | |
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## 📬 Contact |
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If you are interested in custom solutions with edge deployment, please contact [our sales team](https://www.liquid.ai/contact). |
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## Citation |
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``` |
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@article{liquidai2025lfm2, |
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title={LFM2 Technical Report}, |
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author={Liquid AI}, |
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journal={arXiv preprint arXiv:2511.23404}, |
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year={2025} |
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} |
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``` |
